Step-by-step explanation:
are vertically opposite angles.
![\therefore \: \angle PTS\: = \: \angle QTR \\ \\ \therefore \: [11(y - 10)] \degree = (4y - 5)\degree \\ \\ \therefore \:11y - 110 = 4y - 5 \\ \\ \therefore \:11y - 4y = 110 - 5\\ \\ \therefore \:7y = 105 \\ \\ \therefore \:y = \frac{105}{5} \\ \\ \huge \red{ \boxed{\therefore \:y = 15}} \\ \\ \therefore \: m\angle PTS\: =[11(y - 10)] \degree \\ = [11(15- 10)] \degree \\ = [11 \times 5] \degree \\ \huge \orange{ \boxed{\therefore \: m\angle PTS\: = 55 \degree}}](https://tex.z-dn.net/?f=%20%5Ctherefore%20%5C%3A%20%5Cangle%20PTS%5C%3A%20%20%3D%20%5C%3A%20%5Cangle%20QTR%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3A%20%5B11%28y%20-%2010%29%5D%20%20%5Cdegree%20%3D%20%284y%20-%205%29%5Cdegree%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3A11y%20-%20110%20%3D%204y%20-%205%20%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A11y%20-%204y%20%3D%20110%20-%205%5C%5C%20%20%5C%5C%20%5Ctherefore%20%5C%3A7y%20%3D%20105%20%5C%5C%20%20%5C%5C%20%20%5Ctherefore%20%5C%3Ay%20%3D%20%20%5Cfrac%7B105%7D%7B5%7D%20%5C%5C%20%20%5C%5C%20%20%20%5Chuge%20%5Cred%7B%20%5Cboxed%7B%5Ctherefore%20%5C%3Ay%20%3D%20%2015%7D%7D%20%5C%5C%20%20%20%5C%5C%20%5Ctherefore%20%5C%3A%20m%5Cangle%20PTS%5C%3A%20%20%3D%5B11%28y%20-%2010%29%5D%20%20%5Cdegree%20%20%20%5C%5C%20%20%3D%20%5B11%2815-%2010%29%5D%20%20%5Cdegree%20%5C%5C%20%20%3D%20%5B11%20%5Ctimes%205%5D%20%20%5Cdegree%20%5C%5C%20%20%20%20%5Chuge%20%5Corange%7B%20%5Cboxed%7B%5Ctherefore%20%5C%3A%20m%5Cangle%20PTS%5C%3A%20%3D%2055%20%5Cdegree%7D%7D)
Answer:
x=
16
333
y=
8
283
Step-by-step explanation:
1 Solve for yy in 13+2x+y+90=18013+2x+y+90=180.
y=-2x+77y=−2x+77
2 Substitute y=-2x+77y=−2x+77 into 4x+1+8x-2y=1804x+1+8x−2y=180.
16x-153=18016x−153=180
3 Solve for xx in 16x-153=18016x−153=180.
x=\frac{333}{16}x=
16
333
4 Substitute x=\frac{333}{16}x=
16
333
into y=-2x+77y=−2x+77.
y=\frac{283}{8}y=
8
283
5 Therefore,
\begin{aligned}&x=\frac{333}{16}\\&y=\frac{283}{8}\end{aligned}
x=
16
333
y=
8
283
Done
Oranges=r
apples=a
12<em>r</em>+7<em>a</em>=5.36
-12<em>r </em> -12<em>r</em>
What you do on one side you do on both sides
12 on the left cancels out
7<em>a</em>=5.36-12<em>r</em>
/7 /7 /7
Divide 7
7 on the left cancels out
5.36/7=0.76....
left with
<em>a</em>=0.76-12<em>r</em>/7
so the apples cost $0.76 each
to get the cost of the oranges (<em>r</em>) you do the same as you did to get the cost of the apples.
Also on the other equation for 8 oranges and 5 apples you might get different answers but you will see that they are close/similar to the same answers as you will get for the last equations.
Answer:
We know that the equation for the speed is:
Speed = Distance/time.
First, we know that he walks 2 miles in 15 minutes.
distance = 2miles
time = 15 minutes
Then his speed in that interval is:
Speed = (2 mi)/(15 min) = (2/15) miles per minute.
Now, at this same speed, he wants to walk 3 more miles. And we want to find the equation that represents how much time she needs to walk 5 miles (the 2 first miles plus the other 3 miles)
We use again the equation:
Speed = Distance/Time
But we isolate Time, to get:
Time = Distance/Speed
Where:
Distance = 5 miles
Speed = (2/15) miles per min
Time = (5 miles)/((2/15) miles per min) = 37.5 minutes
She needs 37.5 minutes to walk the 5 miles.
